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A244929 Decimal expansion of Ti_2(2+sqrt(3)), where Ti_2 is the inverse tangent integral function. 2
2, 3, 3, 4, 5, 3, 7, 5, 8, 5, 3, 1, 2, 3, 4, 1, 1, 4, 6, 7, 5, 9, 0, 3, 8, 6, 2, 7, 7, 4, 3, 9, 3, 3, 0, 0, 4, 8, 8, 2, 6, 7, 8, 3, 7, 7, 2, 5, 0, 9, 9, 3, 5, 4, 0, 1, 6, 3, 0, 0, 5, 4, 0, 1, 8, 4, 4, 1, 8, 0, 1, 0, 3, 4, 5, 3, 6, 3, 3, 5, 0, 7, 6, 4, 5, 3, 6, 9, 0, 1, 6, 5, 4, 4, 1, 7, 1, 8, 3, 7, 9, 7, 1, 4, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.7.6 Inverse Tangent Integral, p. 57.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

Eric Weisstein's MathWorld, Inverse Tangent Integral

Eric Weisstein's MathWorld, Polylogarithm

FORMULA

2/3*G + 5*Pi/12*log(2+Sqrt(3)), where G is Catalan's number.

Also equals i/2*(polylog(2, -i*(2+sqrt(3))) - polylog(2, i*(2+sqrt(3)))), with i = sqrt(-1).

EXAMPLE

2.3345375853123411467590386277439330048826783772509935401630054018441801...

MATHEMATICA

2/3*Catalan + 5*Pi/12*Log[2 + Sqrt[3]] // RealDigits[#, 10, 105]& // First

PROG

(PARI) default(realprecision, 100); 2/3*Catalan + 5*Pi/12*log(2 + sqrt(3)) \\ G. C. Greubel, Aug 25 2018

(MAGMA) SetDefaultRealField(RealField(100)); R:=RealField(); (2/3)*Catalan(R) + 5*Pi(R)*Log(2 + Sqrt(3))/12; // G. C. Greubel, Aug 25 2018

CROSSREFS

Cf. A006752, A244928.

Sequence in context: A114544 A154726 A325784 * A302920 A280386 A204979

Adjacent sequences:  A244926 A244927 A244928 * A244930 A244931 A244932

KEYWORD

cons,easy,nonn

AUTHOR

Jean-François Alcover, Jul 08 2014

STATUS

approved

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Last modified December 1 12:40 EST 2021. Contains 349429 sequences. (Running on oeis4.)